Exactly, and everything is going as it should (as unusual as this situation is) despite what appears to be concerns on your part.
The Liberals as the incumbent government have the right to face the legislature. Had the vote been
the Liberals would have had every right to strike a deal with the Greens, select a speaker, introduce a Throne Speech, survive a non-confidence vote and stay in power despite being the party in second place. Look up the the 1925 Canadian election as an example.
The NDP and the Greens have struck a deal ahead of time, letting the Liberals know the outcome of a non-confidence vote. If the Liberals want to introduce a Throne Speech that includes every possible Green wishlist item and watch them squirm while voting it down, then they can do so. Everybody would see through that sham but they can do it if they want.
As to your concerns about convention involving the speaker. It is just convention. And I doubt that this situation has ever occurred in BC so it is convention from other parliamentary democracies. I am not even sure how often a speaker has been placed in a position to break a tie in a non-confidence vote, especially when belonging to the opposition party. This situation is so rare convention may not have a whole lot of precedence.
As to the politicizing of the position of speaker. As soon as the Liberals decide that nobody from that party will put their name forward, they are not only breaking with convention (the speaker usually comes from the governing party) but they are doing so for political reasons. They are setting the precedent for the breaking of convention and the politicizing of the position. Don’t blame the NDP or Greens.
The Lieutenant Governor can decide that an election should be called instead but given the NDP/Green agreement and an election barely a month old, that would be highly unusual. Parliament should be given a chance to find a workable government.
As much as you hate the thought of an NDP government supported by the Green party, that is exactly what is going to happen and we will see how long it lasts. For me, this situation gives me more faith in the democratic process than an NDP majority would have. Minority governments make everybody more accountable.